From d56bf4f939d25cea9ac9953b2b0f3237b2dfe8cd Mon Sep 17 00:00:00 2001 From: daHugen Date: Tue, 19 Jul 2022 18:35:13 +0200 Subject: added some equations and made some changes --- buch/papers/lambertw/teil4.tex | 14 ++++++++++---- 1 file changed, 10 insertions(+), 4 deletions(-) (limited to 'buch/papers/lambertw') diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex index e0f7731..6184369 100644 --- a/buch/papers/lambertw/teil4.tex +++ b/buch/papers/lambertw/teil4.tex @@ -237,10 +237,16 @@ Leitet man die Funktion \eqref{lambertw:funkLoes} nach x ab und setzt die Anfang \frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi} &= \eta \\ - x\left(t\right) - &= - \sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} \\ \frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi} &= - \left(\frac{x}{x_0}\right)^2 + \left(\frac{x}{x_0}\right)^2 \\ + x\left(t\right) + &= + \sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} \end{align*} +\begin{equation} + y(t) + = + \frac{1}{4}\left(\left(y_0+r_0\right)\frac{W\left(\chi\cdot e^{\chi\ -\ \frac{4t}{r_0-y_0}}\right)}{\chi}+\left(r_0-y_0\right)\cdot\mathrm{ln}\ \left(\frac{W\left(\chi\cdot e^{\chi\ -\ \frac{4t}{r_0-y_0}}\right)}{\chi}\right)-r_0+3y_0\right) + \label{lambertw:funkNachT} +\end{equation} -- cgit v1.2.1